Quantifying the imaginarity of quantum states via Tsallis relative entropy

It is a fundamental question that why quantum mechanics uses complex numbers instead of only real numbers. To address this topic, recently, a rigorous resource theory for the imaginarity of quantum states were established, and several imaginarity measures were proposed. In this work, we propose a new imaginarity measure based on the Tsallis relative entropy. This imaginarity measure has explicit expression, and also, it is computable for bosonic Gaussian states.